I have to use arithmetic expressions and I need to know if two expressions are equivalent, i.e do they yield the same result and if written slightly different, do they represent the same expression?
For example, $5*7$ is equivalent to $7*5$, or $(4*3 + 3*2) \iff (3*2 + 4*3)$. Yes, division and subtraction are not commutative.
Apart from the result, what else can tell me mathematically that two arithmetic expressions are equivalent? What is the general math answer to this question?